forgive and forget is the right thing to do. but you have to wonder if others still question this person, why? do they know something you don't? or do they just not like this person for some other reason? consider it carefully.
That's a good way of looking at it, but I was working from the point of true repentance... she wrote "Wouldn't it be the christian thing to forgive and forget if they were now doing the right things?" So I'm assuming this girl is no longer doing what she did to earn her rep in the first place... it's good to be cautious if there's reason to suspect that this person is leading a double life, though.